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1 year ago

given the following information, determine which lines, if any, are parallel. state the converse that justifies your answer.

1 answer:

3 0

From the information in the diagram found in a similar question online (please see attached drawing), the parallel lines are;

w||z
x||y
x||y
w||z
w||z
x||y
x||y
w||z
x||y
w||z

<h3>What are the relationships between angles formed by parallel lines?</h3>

Parallel lines are lines that do not meet, when extended indefinitely.

The possible information given as obtained from a similar question posted online are;

1. ‹1 is congruent to ‹5

2. ‹7 is congruent to ‹9

3. m‹8 + m‹9 = 180°

4. ‹16 is congruent to ‹14

5. m‹1 + m‹4 = 180°

6. ‹3 is congruent to ‹13

7. ‹2 is congruent to ‹10

8. ‹11 is congruent to ‹15

9. m‹4 + m‹13 = 180°

10. ‹8 is congruent to ‹6

1. Given that ‹1 is congruent to ‹5 where ‹1 and ‹5 are alternate exterior angles, we have that line w is parallel to line z

w||z

Theorem (converse); Alternate exterior angles formed by two parallel lines having a common transversal are congruent.

2. ‹7 and ‹9 are alternate interior angles.

Given that ‹7 is congruent to ‹9, therefore;

Line x is parallel to line y

x||y

Theorem (converse); Alternate interior angles formed by two parallel lines having a common transversal are congruent.

3. Given that m‹8 + m‹9 = 180°, therefore;

‹8 and ‹9 are supplementary angles, formed between lines x and y.

‹8 and ‹9 are also consecutive interior angles.

Theorem (converse); Consecutive interior angles formed between parallel lines are supplementary.

Therefore;

x||y

4. ‹16 and ‹14 are corresponding angles formed by lines w and z.

Theorem (converse); Corresponding angles formed by parallel lines are congruent.

Given ‹16 congruent to ‹14, we have;

w||z

5. m‹1 and m‹4 are consecutive exterior angles formed by lines w and z.

Theorem (converse); Consecutive exterior angles formed by two parallel lines are supplementary.

Given that m‹1 + m‹4 = 180°, we have;

w||z

6. ‹3 and ‹13 are alternate exterior angles formed by lines x and y.

Theorem (converse); Alternate exterior angles formed by parallel lines are congruent.

Given that ‹3 congruent to ‹13, we have;

x||y

7. ‹2 and ‹10 are corresponding angles formed by lines x and y

Given that ‹2 congruent to ‹10, therefore;

x||y

8. ‹11 and ‹15 are alternate interior angles formed by lines w and z.

‹11 is congruent to ‹15, therefore;

w||z

9. ‹4 and ‹13 are consecutive exterior angles formed by lines x and y

m‹4 + m‹13 = 180°, therefore;

x||y

10. ‹8 and ‹6 are corresponding angles formed by lines w and z.

‹8 is congruent to ‹6, therefore;

w||z

Learn more about angles formed by parallel lines that have a common transversal here:

brainly.com/question/24607467

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PLEASE HELP ASAP!!!!!!!

maria [59]

Answer:

40 cm² = B

178,127514 ≈ LA

218,127514 ≈ SA

Step-by-step explanation:

First and foremost, since we were not given a height, to find the height, take one-third of the area base [area base in this case is ws, since it is a rectangular base]: $\frac{1}{3}(40) = 13 \frac{1}{3}$

This is your height.

Now, to find the lateral area, we use this formula:

$l \sqrt{(\frac{w}{2})^{2} + {h}^{2}} + w \sqrt{( \frac{l}{2})^{2} + {h}^{2}} = L. A.$

Plugging these numbers into this formula will give you an approximate value of 178,127514.

Then you add the lateral area to the base area to get your surface area:

$40 + 178,127514 = 218,127514$

I am joyous to assist you anytime.

7 0

3 years ago

Paul Kim estimates that he will drive about 10,000 miles during the year and will have $3,460 in annual fixed costs. He projects

Mama L [17]

Answer:

The maximum annual variable cost he can have to reach his projection is $1,940

Step-by-step explanation:

Given;

Number of miles drive per year N = 10,000 miles

Total annual Fixed cost F = $3,460

cost per mile(rate) r = $0.54 or less

Total cost = fixed cost + variable cost

Total cost = cost per mile × number of miles

Total cost = r × N = $0.54 × 10,000 = $5,400

Let V represent the total variable cost per year;

F + V ≤ r × N

Substituting the values;

3,460 + V ≤ 5,400

V ≤ 5,400 - 3,460

V ≤ 1,940

The maximum annual variable cost he can have to reach his projection is $1,940

5 0

3 years ago

Janet bought4/5 of a pound of walnuts. Her family ate 1/3 of a pound. How much is left?

Serga [27]

this just wants us to calculate 4/5-1/3

make common denom

4/5 times 3/3=12/15

1/3 times 5/5=5/15

4/5-1/3=12/15-5/15=(12-5)/15=7/15

7/15lb is left

6 0

3 years ago

Read 2 more answers

Multiply (3x – 1)(5x – 9) Show work Please

Murljashka [212]

Answer:

15x^2-32x+9

Step-by-step explanation:

(3x – 1)(5x – 9)

FOIL

first: 3x*5x= 15x^2

outer: 3x(-9) = -27x

inner: -1(5x) = -5x

last: -1(-9) = 9

Add them together

15x^2 -27x-5x +9

Combine terms

15x^2-32x+9

6 0

3 years ago

Read 2 more answers

The probability of drawing two aces from a standard deck is 0.0059. We know this probability, but we don't know if the first car

ivanzaharov [21]

Answer:

Option C is right

C. They are independent because, based on the probability, the first ace was replaced before drawing the second ace.

Step-by-step explanation:

Given that the probability of drawing two aces from a standard deck is 0.0059

If first card is drawn and replaced then this probability would change. By making draws with replacement we make each event independent of the other

Drawing ace in I draw has probability equal to 4/52, when we replace the I card again drawing age has probability equal to same 4/52

So if the two draws are defined as event A and event B, the events are independent

C. They are independent because, based on the probability, the first ace was replaced before drawing the second ace.

4 0

3 years ago